Transverse vibrations of rectangular orthotropic plates with one or two free edges while the remaining are elastically restrained against rotation

A survey of the literature reveals that the title problem has not been previously solved. The fundamentals frequency of transverse vibration of the orthotropic structural element is determined by expanding the displacement amplitude function in terms of simple polynomial coordinate functions which satisfy identically the essential boundary conditions and approximately some of the natural edge requirements.The Ritz method is then used to generate the frequency equations.